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Unformatted text preview: Basic Physics: Gravity and Energy Energy and Momentum Conservation of Momentum Energy and Momentum Conservation of Momentum There is a second fundamental principle in mechanics which follows from Newtons First Law of Motion: Bodies at rest stay at rest until acted on by a force. Bodies in uniform motion maintain that motion until acted on by a force. This Law relates to the idea of inertia. Or, more specifically, in more modern language, it can be stated as another principle of conservation akin to the conservation of energy: In a closed system, momentum is conserved. Momentum, in mechanics, is defined as the product of the mass and velocity, and is often denoted by the symbol p . So we have p=mv. It is worth explicitly restating what we mean by closed. A closed system is one which is not affected by external forces. What does this mean isnt it just the same as the conservation of energy? In brief, no. Energy and Momentum Conservation of Momentum Look again at Newtons First Law of Motion: Bodies at rest stay at rest until acted on by a force. Bodies in uniform motion maintain that motion until acted on by a force. After some thought, you may come to realize that this idea of momentum has a sense of direction. For example, an object moving in a straight line (which is how all objects move in the absence of force!) continues in a straight line. It is not required to do so by energy conservation (it could for example, instantaneously reverse direction and have exactly the same kinetic energy). However, momentum has direction (in the language of physics, it is a vector quantity; energy on the other hand is a scalar quantity) and so reversing the direction of the object changes the sign, and hence value, of the momentum! It is momentum conservation, not energy conservation, which relates to our common sense impression of inertia. Its why your car wont stop on a dime! Energy and Momentum Conservation of Momentum Now consider again our thought experiment of two objects, widely separated, initially at rest. Clearly, at the start, the momentum is 0 (remember, the objects start at rest). Now, let the system run. We have already seen that the objects begin to move toward each other under the force of gravity, and that they move faster and faster. Ok, hold on. Momentum is the product of mass and velocity. As soon as the objects start moving, isnt the momentum increasing? No, it doesnt its still 0! Because of the directionality of momentum, the total momentum remains zero since the two objects are moving in opposite directions. Energy and Momentum Conservation of Momentum There is one further concept worth considering regarding momentum. This is the idea of angular momentum related to the momentum we have just discussed. Without exploring details, angular momentum can be thought of as the inertia of rotation. It is also a conserved quantity....
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 Fall '08
 Gladders

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